Method of measuring displacement between points on a test object

ABSTRACT

A test object is analyzed electronically, i.e. without the use of photographic film. The invention generates a pair of laterally-displaced images of the object which interfere with each other to produce a pattern that can be recorded without a high-resolution detector. The object is illuminated with at least partially coherent light. Reflected light from the object is directed through a birefringent material, a lens system, a polarizer, and then to an image detector, such as a video camera. The birefringent material causes non-parallel beams originating from a unique pair of points on the object to become nearly parallel, and orthogonally polarized. The polarizer modifies the polarization of the parallel beams so that they will interfere with each other. Because the intefering light beams are nearly parallel, the spatial frequency of the interference pattern is sufficiently low that the pattern can be recorded by a low-resolution detector, such as a video camera. Interference patterns due to the superposition of two laterally-displaced images of the same object are recorded while the object is in an undeformed and a deformed state. A computer compares these interference patterns and produces a resultant pattern which depicts the deformation of the test object. Because photographic film is not needed, the invention can analyze objects very rapidly. Also, since the interference pattern is derived from pairs of distinct points on the object, the invention directly provides information on strain.

This is a division of application Ser. No. 07/129,709, filed Dec. 7,1987, now U.S. Pat. No. 4,887,899.

BACKGROUND OF THE INVENTION

This invention comprises a method and apparatus for nondestructivelyanalyzing a test object. The invention is especially useful fordetecting minute defects in manufactured parts. Defects in objectsusually induce strain anomalies which can be identified from the fringepatterns produced by this invention. The invention may also be used forother purposes. For example, the invention comprises an ultra-sensitive,whole-field strain gauge, which permits strain distribution of a largearea to be measured without the need for conventional gauges ortransducers.

One method, known in the prior art, for analyzing a test object is"shearography". According to this method, two laterally-displaced imagesof the object are made to interfere to form a pattern of fringes. Thepattern is random, and depends on the characteristics of the surface ofthe object. When the object is deformed, by temperature, pressure, orother means, the random interference pattern will change. The amount ofthe change depends on the soundness of the object. A comparison of thefringe patterns for the deformed and undeformed states gives informationabout the structural integrity of the object. The method is calledshearography because the one image of the object is laterally-displaced,or sheared, relative to the other image.

An example of a method for practicing the technique of shearographyappears in U.S. Pat. No. 4,139,302, the disclosure of which isincorporated by reference herein. In the latter patent, the shearing isaccomplished by placing the wedge-shaped prism along a portion of alens. The light beams which pass through the prism are displacedrelative to the beams which do not pass through the prism. Thus, thelens and wedge system produces two laterally-displaced images of theobject.

The main disadvantage of methods for shearography of the prior art isthe high spatial frequency of the patterns produced. Spatial frequencymeans the number of fringe lines per unit length. When the spatialfrequency is too high, it is necessary to record the interferencepattern on high-resolution photographic film. It will be shown laterthat the spatial frequency of a fringe pattern is given by

    f=(2 sin (α/2))/λ

where

α=the angle made by two interfering rays, and

λ=the wavelength of the light.

Because λ is normally very small compared with the value of α, thespatial frequency can become quite large. For example, if α=20°, and ifλ=0.5 microns, then the spatial frequency is about 700 lines permillimeter. It is not possible to view patterns having such fine detailwith a video camera instead, one must use a high-resolution photographicfilm.

In some cases, one might try to reduce the spatial frequency by reducingα, such as by increasing the distance between the lens and the image.But the latter procedure would have the effect of greatly magnifying theimage, and is therefore, at best, unwieldy, and, at worst, virtuallyunworkable. When the image and lens are moved far apart from each other,the image becomes so large that a video camera would need to scan theimage almost point by point. Moreover, the overall intensity of thepattern would decrease, requiring a coherent light source of higherpower, Also, in a wedge-shearing system, the interfering beams come fromtwo halves of the lens, and thus the angle between the interfering beamsis inherently large. Thus, the wedge-shearing technique inherentlyproduces an interference pattern of high spatial frequency which isbeyond the resolving capability of a video camera.

Another disadvantage of wedge-shearing technique is the need for opticalfiltering of the interference pattern. The high spatial frequency of thefringes produced by wedge system makes the fringes very difficult toview with the naked eye. It therefore becomes necessary to provide anoptical high-pass filter, which blocks out the low-frequency fringes,and which produces a pattern having visible dark bands corresponding todefective areas on the test object. Because it requires the use ofphotographic film, and because it also requires post-recording opticalfiltering, the wedge-shearing method is very cumbersome and slow whenused for the inspection of objects. In general, it cannot fulfill thespeed demands of a typical industrial production line.

Details of the high-pass optical filter used int eh wedge-shearingtechnique are given int he article of Y. Y. Hung, entitle "Shearography:a New Optical Method for strain Measurement and Nondestructive Testing",in Optical Engineering, May-June, 1982, vol. 21, No. 3, pages 391-5. Thelatter article is incorporated by reference herein.

One method of the prior art which avoids the problems due to excessivelylarge spatial frequencies is the techniques is the technique known aselectronic speckle pattern interferometry (ESPI). An example of thelatter technique is described in U.S. Pat. No. 3,816,649, the disclosureof which is also incorporated by reference herein. In ESPI, a beam ofcoherent light is directed onto the test object and reflected onto animage sensor. At the same time, a reference beam is also directedtowards the sensor. The reference beam may be a "pure" beam or it may byreflected from a "reference" object. Both the object beam and thereference beam are nearly parallel, when they reach the image sensor, sothe spatial frequency of the interference fringes is relatively low,Thus, the image sensor can be a video camera, or its equivalent.

While ESPI makes it possible to view an interferences pattern directlywith a video camera, it has important disadvantages. ESPI is similar toconventional holography, in that it requires an object beam and areference beam of coherent light. The presence of two distinct beamsincreases the complexity of the optical system. The ratio of intensitiesof the object and reference beams must be carefully controlled, and thepath lengths of the beams must be matched. Perhaps most importantly,ESPI, like holography, is very sensitive to vibration. The slightestmovement of either the object or the apparatus for guiding the referencebeam can ruin the pattern. Thus ESPI requires special vibrationisolation precautions, and is not practical for inspection ofmanufactured parts in a factory environment, or in the field.

Furthermore, ESPI measures absolute surface displacement, whereas thepresent invention measures relative displacement which is directlyrelated to strains. Since defects in objects normally produce strainconcentrations, it is easier to correlate defects with strain anomaliesthan with displacement anomalies.

The present invention overcomes the disadvantages of the prior art,described above, by providing a method and apparatus for analyzing atest object, without the need for photographic film, and using only onebeam of light. With the present invention, the interference patterns canbe recorded directly by a video camera, or other electronic imagesensor, and process by a computer, without intermediate developing andoptical filtering steps. Thus, the invention can analyze objects at avideo rate, i.e. up to about 30 frames per second. The output of thecamera can be connected to a computer, which can store and analyze thedata very rapidly. Thus, the invention is capable of inspecting objectsat the rapid rate demanded by a typical production process.

Because only one beam is needed, the patterns obtained with the presentinvention are relatively insensitive to vibrations of the apparatus. Theinvention can therefore be used in typical production and fieldenvironments without special vibration isolation equipment. Thesingle-beam process also eliminates the complex optical alignmentproblems associated with ESPI.

The present invention also provides means for measuring strains in atest object with extremely high precision. The invention can thereforebe used as a whole-field strain gauge, and is not limited to sue intesting for defective objects.

The present invention also provides means for measuring the amplitudegradient in a steadily vibrating object. Measurement of gradients in theamplitude of vibration provides information on the maximum displacementsof the vibrating object. The invention also provides means for measuringtransient strains in an object.

SUMMARY OF THE INVENTION

The apparatus of the present invention includes a source of coherent, orpartially coherent radiation, including, but not limited to, visiblelight, which is directed onto a test object. The light reflected fromthe object passes through an optical system which, in the preferredembodiment, includes a birefringent material, a lens, and a polarizer.After passing through the optical system, the light enters an imagedetector, which can be that of a video camera or equivalentphotoelectric device. The image detector is connected to a computer, orits equivalent, which can store and analyze each frame of data.

The birefringent material produces a sheared image. The material, whichcan be a calcite crystal, separates an incoming beam into two distinctbeams, polarized in mutually orthogonal directions, and which propagatethrough the material with different velocities. There exists a uniquepair of points on the object, such that light beams reflected from thesepoints become nearly parallel after passing through the birefringentmaterial.

A lens focuses the light leaving the birefringent material onto an imageplane. Before reaching the image plane, the light passes through thepolarizer, which resolves the mutually orthogonally-polarized beams intocomponents which are polarized in the same direction. The pairs of beamsleaving the polarizer can thus interfere with each other, and theyproduce an interference pattern on the image plane.

Because the pairs of beams, originating from pairs of distinct points onthe object, arrive at the image plane as nearly parallel beams, thespatial frequency of the interference pattern is relatively low, and theimage detector need not be capable of extremely high resolution. Theimage detector can therefore be an ordinary video camera or equivalentdevice. The camera is connected to a computer for rapid analysis of thedata.

In another embodiment, a quarter-wave plate is inserted between thebirefringent material and the polarizer. The effect of this arrangementis to shift the phase of the resulting interference pattern. The amountof the phase shift is varied by adjusting the orientation of thepolarizer. The ability to perform this phase shift allows theinterference pattern, and thus the deformation in a test object, to beexamined with great precision, and enables the invention to be used, forexample, as an ultra-sensitive, whole-field strain gauge.

It is also possible to insert a narrow band pass optical filter, whichadmits only the coherent illumination, between the object and thebirefringent material, thereby preventing virtually all ambient lightfrom entering the image sensor, and allowing the invention to be usedeven in sunshine.

Another quarter-wave plate may be interposed between the object and thebirefringent material, or between the band pass filter, if used, and thebirefringent material, to insure that the light entering thebirefringent material is circularly polarized. The latter polarizationtends to equalize the amplitude of all beams transmitted by thebirefringent material.

It is therefore an object of the present invention to provide a methodand apparatus for nondestructive testing of objects.

It is another object to provide a testing method and apparatus whichdoes not require the use of photographic film, and wherein the imagedetector can be a video camera, or equivalent device.

It is another object to provide a testing method and apparatus wherein acomputer can be easily used to rapidly analyze the data.

It is another object of the invention to reduce the time and expenserequired in the inspection of objects.

It is another object to provide a method for nondestructive testingwherein interference patterns are detected in "real time" by an imagesensing device.

It is another object to provide a method and apparatus fornondestructive testing, wherein objects can be analyzed at a video rate.

It is another object to provide an apparatus as described above, whereinthe apparatus does not require special vibration isolation.

It is another object to provide an apparatus and method for testing ofarticles, wherein only one light beam is required.

It is another object to provide a testing method which is sufficientlyrapid to be used in a typical production process.

It is another object to provide a testing method and apparatus which isreadily adapted for measuring differential anomalies in the test object.

It is another object to provide an apparatus and method for accuratelymeasuring strains.

It is another object to provide an apparatus and method, as describedabove, wherein the phase of the interference pattern generated by theobject can be adjusted, and wherein the interference pattern can beanalyzed with great precision.

It is another object to provide an apparatus and method which can beused to analyze test articles in the field, or in a factory, where strayvibrations are present, and wherein the apparatus is negligibly affectedby ambient light.

Other objects and advantages of the invention will be apparent to thoseskilled int he art, from a reading of the following brief description ofthe drawings, the detailed description of the invention, and theappended claims.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a diagram, use dint he derivation of the equation for spatialfrequency, showing two light beams, from point sources, interfering on ascreen.

FIG. 2 is a schematic diagram illustrating the transmission of lightbeams, from two distinct points on a test object, through a birefringentmaterial.

FIG. 3 is a schematic diagram illustrating the splitting of an incidentbeam into two beams, by a birefringent material.

FIG. 4 is a schematic diagram of one embodiment of the presentinvention.

FIG. 5 is a schematic diagram of another embodiment of the presentinvention, wherein the phase of the interference pattern can beprecisely controlled.

FIG. 6 is a diagram illustrating the polarization of a beam of lighttraveling from a birefringent material, through a quarter-wave plate,and through a polarizer.

FIG. 7 is a diagram illustrating the action of the quarter-wave plateused in the invention.

FIG. 8 is a diagram illustrating the action of the polarizer used tocontrol the phase of the interference pattern, in the present invention.

DETAILED DESCRIPTION OF THE INVENTION

The present invention is essentially a shearographic technique. That is,the invention generates two laterally-displaced images of the testobject which interfere with each other to produce a fringe pattern.Comparison of two such patterns, for two distinct states of deformation,yields information on the condition of the surface of the object.

As explained above, shearographic techniques of the prior art requirehigh-resolution photographic film because of the high spatial frequency,i.e., the number of fringes per unit length, of the interferencepattern. The relationship between the spatial frequency, the anglebetween interfering beams, and the wavelength of the light is derived asfollows.

Consider the classical Young's experiment, involving the interference oflight beams from two point sources A and B, illustrated in FIG. 1. A andB are separated by distance d. Assume that the beams from points A and Bmeet at a point P(x,y,z) on a distant screen. An interference patternconsisting of parallel fringe will be observed.

The interference pattern can be described by

    I=a.sup.2 (1+ cos θ)                                 (1)

where I is intensity, and a is the amplitude of the light. θ is relatedto the optical path difference by ##EQU1## where λ is the wavelength ofthe light, and ##EQU2## Thus, ##EQU3##

Using the approximation PB≈PA, since the screen is assumed to bedistant, we obtain ##EQU4##

Dark fringes occur where

    1+ cos θ=0

or θ=Nπ, N=1,3,5, . . .

Thus, the difference, in θ, between two adjacent dark fringes, is 2π, sothe spacing between two adjacent dark fringes at x₁ and x₂ is obtainedfrom ##EQU5##

Thus, ##EQU6## and the spatial frequency is given by ##EQU7##

Thus, the spatial frequency of the fringe pattern is approximately##EQU8##

The essence of the present invention is therefore to produce aninterference pattern wherein the effective value of α is sufficientlysmall that the spatial frequency given by Equation (5) is within theresolving power of a video camera or other, non-photographic sensor. Theapparatus of the invention, in effect, creates two, laterally-displacedimages of the object, the images being made to interfere with each otherto form a fringe pattern having a reasonably low spatial frequency.

The means of generating the shearing effect is preferably a birefringentmaterial, such as a calcite crystal, or any other material or meanswhich exhibits double refractivity. A birefringent material has twoprincipal axes of transmission, which separate an incident light beaminto two beams, having different velocities within the material. Thesebeams are polarized int he mutually-orthogonal directions of theprincipal axes of the birefringent material, and are known as theordinary beam and the extraordinary beam. The splitting of one beam intotwo is illustrated schematically in FIG. 3. FIG. 3 shows birefringentmaterial 8, schematically symbolized by a trapezoid, and incident beam2. The incident beam is split into ordinary beam 4 and extraordinarybeam 6. The dots indicate the ordinary beam and the bars indicate theextraordinary beam. Thus, when light from an object passes through abirefringent material, two laterally-displaced images will be formed onan image plane.

More detailed information about birefringent materials, includingcalcite, is found in the article entitled "Laser Polarizers", in TheOptical Industry and Systems Purchasing Directory (1982). The latterarticle is incorporated by reference herein.

For purposes of understanding the present invention, it is helpful toview the transmission of light through a birefringent material inanother way. The passage of light rays through an optical system isreversible; one can rename the incident beam as the transmitted beam,and vice versa. Since a birefringent material separates one beam intotwo distinct, non-parallel beams, it is also true that there are twounique beams which, after passing through the birefringent material,become parallel. This phenomenon is illustrated in the schematic diagramof FIG. 2.

FIG. 2 shows object 1 and birefringent material 3. Light beams 5 and 7,originating from a source (not shown) of coherent, or partiallycoherent, light are reflected from the object, and enter thebirefringent material. The transmitted beams substantially coincide, asillustrated by beam 9. These beams are polarized in mutually-orthogonaldirections, and will therefore not interfere with each other.

There are two, and only two, points on the object, from which lightbeams will be reflected so as to produce a given pair of nearly paralleltransmitted beams. Indeed, the entire object can be conceptualized as aset of unique pairs of points which give rise to pairs of nearlyparallel beams. The qualifier "nearly" is used because, in practice, thelight scattered from an object point travels in cones, not parallelbeams, and, due to slight variations in the optical properties of thebirefringent material resulting from varying angles of incidence, mostof the pairs of beams leaving the material are not exactly parallel.

FIG. 4 is a schematic diagram of one embodiment of the presentinvention. Laser 11 illuminates object 13, and the light is reflectedfrom the object. The surface of the object can be diffusely reflectiveor specularly reflective. The reflected light passes through an opticalsystem which includes birefringent material 15, lens 17, and polarizer19. The lens focuses the light onto the image plane of image sensor 21,which can be that of a video camera. The image sensor is connected tocomputer 23 for analysis of the data. The computer includes appropriatecircuitry for recording, digitizing and processing the information ineach image or frame. The computer is connected to a display device 24.

Reflected light beams 25 and 27, originating from distinct points 29 and31 on the test object, pass through the birefringent material, and leavethat material as nearly parallel, but orthogonally-polarized beams.Polarizer 19, whose polarization axis is oriented at 45° to theprincipal axes of the birefringent material, resolves each beam into acomponent which is polarized in a direction 45° away from the directionof original polarization. The result is a pair of parallel beamspolarized in the same direction, though having a reduced amplitude. Theparallel beams can therefore interfere, and will create an interferencepattern on the image sensor. What is shown for two points and two beamsoccurs simultaneously for all the pairs of points on the object.

Because each point on the image plane receives light from two distinctpoints on the object, the interference pattern is equivalent to thesuperposition of two laterally-displaced, or sheared, images of the testobject.

The invention is not limited to use with visible light. The inventioncan be practiced with infrared or ultraviolet radiation, or even X-rays.The invention requires only the use of some kind of radiation which iscapable of interference. It is therefore understood that, in thisspecification, the term "light" is intended to include all such otherforms of radiation.

The invention is also not limited by the type of object being studied.The test object can be made of any material, and can include biologicaltissues and organs.

The lens can be located virtually anywhere in the system. For example,it could be placed between the object and the birefringent material,between the birefringent material and the polarizer, or between thepolarizer and the image sensor. Indeed, if the image sensor is a videocamera, lens 17 could be the camera lens, Thus, it is understood thatthe placement of the symbol for the lens, in the figures, is onlyexemplary, and not limiting. Also, the lens can be a simple lens or acompound lens.

Because of the irregular texture of he surface of the object, theinterference pattern is of random character. Nevertheless, the randominterference pattern acts as an information carrier about the state ofdeformation of the test object. When the object is deformed, or deformedfurther from a previous deformed state, the interference pattern isslightly modified. By comparing the interference patterns of the testobject in two slightly deformed states, another fringe pattern isobtained which depicts the surface deformation. The latter fringepattern is sometimes called a secondary fringe pattern. The secondaryfringe pattern does not result from direct optical interference; rather,it is the result of a comparison performed by a computer programmedaccording to one of the algorithms explained later.

The interference patterns must by analyzed by a computer, or anequivalent device. Although it is possible to observe directly, on avideo monitor, the individual interference patterns for the two statesof deformation, it is only by comparing these two patterns that theinformation on the difference in the states of deformation of the objectwill be revealed. This comparison cannot normally be done by the eyealone.

Apart from the need form a computer to observe the interferencepatterns, the computer is also useful for purposes of storing manyimages, or selected images, for later processing.

It is understood that, in the context of this invention, the term"computer" may include many types of devices, including different typesof microprocessors having varying amounts of memory capacity. The termis also intended to include any device capable of performing comparisonsbetween pairs of images.

Thus, the operation of the invention can be summarized as follows. Acoherent or partially coherent light beam is directed onto the testobject, and an interference pattern is observed and/or recorded. Thenthe object is stressed, such as by applying heat, pressure, vibrationalexcitation, or any other means of applying stress. Another interferencepattern is obtained. Comparison of the interference patterns, for thestressed and unstressed conditions, yields information about theintegrity of the test object. Note that the initial condition of theobject may be one of stress, and that the interference pattern may beobtained by applying further stress. The invention compares the patternsobtained for two distinct conditions of stress, one of which may be thespecial case of zero stress.

FIG. 5 shows an alternative embodiment of the invention. Light fromsource 42 is reflected from test object 40, and directed throughbirefringent material 44, lens 46, and polarizer 48. The image isreceived by image sensor 50, connected to computer 52 and display device54. As before, the term "light" is used to mean any form of radiationwhich is capable of interference, and the lens can be placed anywherebetween the object and the image sensor. All of the components discussedso far are similar to those shown in FIG. 4. The embodiment of FIG. 5also includes band-pass optical filter 56, quarter-wave plate 58, andquarter-wave plate 60.

Band-pass filter 56 is chosen to pass only the frequency of the coherentlight of the illumination, reflected from the object. Virtually allambient light is rejected. Thus, use of the filter enables the apparatusto operate where the ambient light is very intense, even in sunshine.

Quarter-wave plate 58 is useful in the case where the light reflectedfrom the object is linearly polarized. In the latter case, the principalaxes of the birefringent material would need to be oriented by 45° tothe plane of polarization of the reflected beams, in order to insurethat the two beams exiting the birefringent material are of nearly equalintensity. Quarter-wave plate 58, placed before the birefringentmaterial, makes the incident beam circularly polarized, and insures thatthe intensities of the components transmitted by the birefringentmaterial will be nearly equal. Quarter-wave plate 58 thus avoids theneed for a particular orientation of the birefringent material.

Quarter-wave plate 60 operates in conjunction with polarizer 48 tocontrol the phase of the interference patter. A complete discussion ofthe function of quarter-wave plate 60 will be given later.

The band-pass filter, the first quarter-wave plate 58, and the secondquarter-wave plate 60, shown in FIG. 5, are all optional. Moreover,these three components work independently, and any combination of themmay be used. The band-pass filter can be placed anywhere between theobject and the image sensor. If quarter-wave plate 58 is used, it shouldbe placed between the object and the birefringent material. Quarter-waveplate 60, if used, must be located between the birefringent material andthe image sensor.

The interference patterns produced by the apparatus of either of FIGS. 4or 5 can be analyzed by the following technique. Let the wavefronts ofthe sheared images received by the image sensor be given by

    μ(x,y)=ae.sup.θ(x,y)                              (6a)

and

    μ(x+δx,y)=ae.sup.θ(x+δx,y)            (6b)

where θ(x,y) and θ(x+δx,y) represent the phase of the light from a pointP(x,y) and a neighboring point P(x+δx,y), respectively, and a is theamplitude of the light. The amplitude is assumed to be equal for the twoneighboring points.

The total light amplitude U_(T) received by the image sensor is thus

    U.sub.T =μ(x,y)+μ(x+δx,y)                      (7)

and the intensity I_(u) of the image is

    I.sub.u =U.sub.T U.sub.T *=2a.sup.2 [1+ cos φ]         (8)

where φ=θ(x,y)-θ(x+δx,y) represents a random phase angle. The phaseangle φ is random because the object surface is generally opticallyrough, and its surface depth variation is irregular. I_(u) represents animage of the object, modulated by a random interference pattern (RIP)due to the random phase angle.

When the object is deformed, the surface displacements cause a change inthe optical pat. This optical path change produces a relative phasechange between the two sheared wavefronts, the RIP is slightly modified.Thus, Equation (8) becomes

    I.sub.d =2a.sup.2 [1+ cos (φ+Δ)]                 (9)

where I_(d) is the intensity distribution after deformation, and Δ isthe relative phase change due to relative displacement between thepoints P(x,y) and P(x+δx,y). The relationship between the relative phasechange and the relative displacements will be described later.

To generate the fringe pattern which illustrates the condition of thetest object, I_(u) is first digitized and stored in a computer memory.Then, the object is deformed, or deformed further from an initialdeformed state, and the deformed image I_(d) is also digitized andstored. I_(u) and I_(d) are compared by any one of the followingtechniques, performed by a computer or its equivalent:

1. Subtraction

This is the simplest technique for analyzing the test object. Thecomputer determines a resultant intensity distribution I, where I=I_(d)-I_(u), or

    I=2a.sup.2 [ cos (φ+Δ)- cos φ]               (10)

The intensity distribution shown in Equation (10) represents a secondaryinterference pattern depicting Δ, which is related to the deformation.This fringe pattern can be displayed on a monitor, by the computer, andcan be interpreted directly with the naked eye. Equation (10) shows afringe pattern having dark lines where Δ=Nπ, where N is an even integer,and having bright lines where Δ=Nπ, where n is an odd integer.

2. Addition

The computer can be programmed to calculate the sum of I_(d) and I_(u).The result is

    I=2a.sup.2 [2+ cos (φ+Δ)+ cos φ]             (11)

Equation (11) shows that there is a fringe pattern with darker lines forΔ=Nπ, where N is an odd integer, and brighter lines for Δ=Nπ, where N isan even integer.

The pattern obtained from addition of I_(u) and I_(d) is not as easy toobserve as the pattern obtained from subtraction, because even the"dark" lines are relatively bright. However, if the computer isprogrammed to subtract away the constant term in Equation (11), theresult can be made easily visible. Other image enhancement techniquesmay also be used to increase further the contrast of the fringe pattern.

3. Multiplication

In this case, the intensity distributions are multiplied together. Theresult is ##EQU9## Equation (12) defines a pattern having darker fringelines for Δ/2=Nπ, where N is an odd half-integer (i.e. 1/2, 3/2, 5/2, .. . ), and brighter fringe lines for Δ/2=Nπ, where N is an integer. Asin the case of addition, the pattern represented by Equation (12) is notas easy to observe directly as in the case of subtraction.

4. Division

The quotient of the deformed and non-deformed intensities is given by##EQU10## Equation (13) defines a fringe pattern having dark lines forΔ/2=Nπ, where N is an integer. Bright fringe lines occur when Δ/2=Nπ,where N is an odd half-integer. The dark lines correspond to the absenceof the random interference pattern (RIP), and the bright linescorrespond to maximum visibility of the RIP.

The technique of analyzing the object by division, as shown above,enjoys the advantage that it is independent of the illumination andreflectivity of the object. That is, when I_(d) is divided by I_(u), thelight intensity distribution a² cancels out, resulting in a uniformimage intensity modulated by a fringe pattern. In practice, theillumination and reflectivity may vary from one point of the object toanother. By using the division technique, the result is made independentof the illumination and reflectivity. The division technique isespecially useful if one needs to obtain a very uniform image, and whereone seeks to pseudo-color code the resultant fringe pattern. Colorcoding aids in the visual identification of anomalies in the fringepattern. When color coding is used, it is important that the pattern notbe disturbed by variations in light intensity along the object.

The relationship between the relative phase change Δ and the relativedisplacement is explained in the paper by Hung, cited above.

The cited publication shows that the relative phase change is given by

    Δ=2π/λ(Aδμ+Bδv+Cδw)   (14)

where (δμ, δv, δw) is the relative displacement vector between P(x,y)and P(X+δx,y). A, B, and C are sensitivity factors which are related tothe position of the illumination point (S(x_(s), y_(s), z_(s)) and thecamera lens position S(x₀, y₀, z₀) by: ##EQU11## where

    R.sub.o.sup.2 =x.sub.o.sup.2 +y.sub.o.sup.2 +z.sub.o.sup.2

    R.sub.s.sup.2 =x.sub.s.sup.2 +y.sub.s.sup.2 +z.sub.s.sup.2

In the case where the magnitude of shearing is small, the relativedisplacements, divided by the distance between the points of interest,approximate the derivative of displacement with respect to the directionof shearing. Note that the derivative of displacement is directlyrelated to the strain of the object. Therefore, the present invention isparticularly suited to providing a direct indication of strain, withoutthe need for further processing.

In general, Equation (14) has three unknown variables. In order toseparate the relative displacements δμ, δv, and δw, one must perform theanalysis three times, each time with a different camera position and/orillumination point, so as to provide a different camera set ofcoefficients A, B, and C. One then obtains three simultaneous equationswith three unknowns. Thus, in the three-dimensional case, six exposuresare required to determine the strain vector (two exposures for eachmeasurement of Δ). The quantities A, B, and C, can be treated asconstants for a given point (x,y,z). That is, A, B, and C areindependent of the strain on the object. Of course, A, B, and C arefunctions of x, y, and z, and must be recomputed when it is desired toanalyze the strain at another point.

The invention is also applicable to the measurement of the relativedisplacements in a test object which is undergoing steady-statevibration. Since in a steadily vibrating object, the object spends mostof its time near the two extreme positions (the positions of maximumamplitude of vibration), the fringe pattern obtained depicts the maximumrelative displacements of the vibrating object. The pattern obtained is,in effect, a time-averaged pattern, and it is a bit blurred compared tothe patterns obtained for a non-vibrating object. But it is stillpossible to observe fringes.

The invention is also applicable to the measurement of transientrelative displacements in the test object, such as those induced byimpact. In this case, a pulsed laser which emits a radiation pulse ofvery short duration (e.g. of the order of 20 nanoseconds) is needed tocapture this transient deformation. In one such procedure, one firstdirects a first pulse at the object, and records the interferencepattern. One then strikes the object, and then directs a second pulse atthe object. The two patterns are compared as before. In the latterprocedure, it is assumed that the laser is charged separately for thetwo pulses. It is also possible to direct a steady train of laserpulses, having a temporal separation of the order of about 1 msec, andto record the images obtained from each pulse.

As stated above, the quarter-wave plate 60 is used, together withpolarizer 48, to adjust the phase of the interference pattern. Phaseshifting is important in cases where it is necessary to analyze thefringe pattern very precisely. Due to irregularities in the pattern, itis usually not possible to identify precisely the gradations ofbrightness of portions of the fringes. The only portions of the fringeswhich can be identified with great precision are the brightest ordarkest regions, i.e. the maxima and minima. Phase shifting of thepattern makes it possible to insure that a point of interest, on theimage plane, will have a maximum or minimum level of brightness. Theamount of phase shift can then be used to infer the relativedisplacement between the two points of interest on the object, thusproviding information on strain.

The theory underlying the controlled phase shifting is explained withthe aid of FIGS. 6, 7, and 8. FIG. 6 schematically illustrates thebirefringent material, the quarter-wave plate 60, and the polarizer. Aquarter-wave plate is a material which has two axes of transmission, andwhich converts an incident beam into two orthogonally-polarized beams,wherein there is a phase difference of 90° (i.e. one quarter-wave)between the two beams. Quarter-wave plates are commercially available.The axes of polarization by a quarter-wave plate are known as the "fast"axis and the "slow" axis. The terms "fast" and "slow" refer only to thefact that the phase of one of the transmitted beams lags that of theother transmitted beam.

For best results, the fast axis of the quarter-wave plate of FIG. 6 isoriented at 45° with respect to the principal axis "1" of thebirefringent material, or "plate". Other orientations can be used, butthe results will not be optimal.

Assume that the wavefronts transmitted through the principal axes "1"and "2" of the birefringent plate are u₁ and u₂, respectively, where u₁represents light originating from the object point P(x,y) and u₂originates from neighboring point P(x+δx,y). The two wavefronts may berepresented by

    μ,(x,y)=a cos wt                                        (16a)

and

    μ.sub.2 (x+δx,y)=a cos (wt-φ)                 (16b)

where a is the amplitude of the light, w is the angular veolcity of thelight wave, t is time, and φ=θ(x+δx,y)-θ(x,y) is a random phase anglerepresenting the relative phase difference between two neighboringpoints.

The wavefronts emerging from the quarter-wave plate, whose fast axis isoriented at 45° to the principal axis "1" are obtained by resolving thecomponents of u₁ and u₂ which lie parallel to the fast axis. FIG. 7illustrates this resolution. The wavefront u_(f) emerging from the fastaxis is ##EQU12## The wavefront u_(s) emerging from the slow axis isretarded by π/2, relative to the wavefront transmitted through the fastaxis. Thus, ##EQU13##

Now, consider the effect of the polarizer. Assume that the polarizer isoriented so that its polarizing axis is oriented at an angle β to theslow axis. The wavefront transmitted through the polarizer is obtainedby resolving the components of u_(f) and u_(s) along the polarizingaxis, as shown in FIG. 8. The wavefront u_(p) transmitted through thepolarizer is thus ##EQU14## Thus, the intensity of the transmitted waveis

    I.sub.p =2a.sup.2 sin.sup.2 (φ/2+β)               (20)

Equation (20) shows that a phase shift β is introduced between the twowavefronts derived from the two neighboring points P(x,y) and P(x+δx,y). The amount of phase shift is controlled simply by adjusting theorientation angle δ of the polarizer.

Note that the ability to control the phase of the interference patterndepends not only on the presence of quarter-wave plate 60 and thepolarizer, but also on the birefringent material. It is the birefringentmaterial which provides the two orthogonally-polarized beams enteringthe quarter-wave plate. With shearing techniques of the prior art, suchas the wedge-shearing method, it is not possible to control the phase ofthe final pattern.

Knowledge of the phase of the interference pattern is a powerful tool.For example, it converts the apparatus of the present invention into anultra-sensitive strain gauge. A method for measuring strain near a givenpoint on the object is as follows. First, from a knowledge of thegeometry of the arrangement, including the position of the birefringentmaterial, the computer calculates the position, on the image plane,corresponding to the given point on the object. The object isilluminated, and a first fringe pattern is recorded and stored by thecomputer. Then, the object is deformed. While the object is in itsdeformed state, the computer continually samples the fringe patternproduced, and compares each such pattern with the pattern originallystored, to produce a secondary fringe pattern (using one of thealgorithms discussed above). Meanwhile, the orientation of the polarizeris adjusted (either manually or automatically) until the secondaryfringe pattern yields a maximum or minimum on the point of interest onthe image. The value of β in Equation (20) is known directly, from theorientation of the polarizer.

Assume now that the algorithm used to generate the secondary fringepattern is subtraction. It has been observed that bright lines on thesecondary fringe pattern occur for Δ=Nπ, where N is an odd integer,Comparison of Equation (20) with Equation (9) shows that the effect ofthe phase shift is to add 2β to Δ, in Equation (9). This means that thecondition for a maximum is Δ+2β=Nπ, where N is an odd integer.

It is possible to calculate N directly, by observing the fringe pattern,and counting the number of ridges from the boundary of the pattern tothe point of interest.

From a knowledge of N, and a knowledge of β, one can readily calculateΔ. Then, using Equation (14), one can calculate the relativedisplacements. A similar technique can be used if the comparisonalgorithm is other than the subtraction method.

The present invention provides significant advantages over theinterferometric techniques of the prior art. Unlike the wedge-shearingtechnique described above, the present invention can be used with avideo camera, a charge-coupled device, or equivalent, and does notrequire high-resolution photographic film. The invention thereforeeliminates the cost of the film, and eliminates the time required fordeveloping the film. Moreover, unlike the wedge-shearing process, thepresent invention does not require subsequent optical filtering to makethe interference patterns visible. Thus, with the present invention,objects can be tested at a video rate. As many as about 30 images persecond can be recorded. The present invention therefore provides a meansfor testing in "real time", and thus can be operated at a speedsufficient to fulfill the demands of a typical production line. Sincethe data are analyzed, in the first instance, by computer, it is veryeasy to store all or some of the incoming data, for further analysis.

As explained above, the present invention permits the precisemeasurement of strains, due to the ability to adjust the phase of theinterference pattern. The prior art does not have this advantage. Unlikeconventional strain gauges of the prior art, which are mounted only atone point of interest, and which give information only about that point,the strain gauge of the present invention can analyze any point on theobject without the need to adjust the position of a sensor. The systemanalyzes the strain at a given point by computer analysis of the imagesproduced, without moving a physical component.

Another advantage of the present invention is that it does not requiresa high-power light source. This advantage is due to the fact that avideo camera, or equivalent electronic device, is much more sensitivethan a high-resolution photographic emulsion. A video camera equippedwith an image intensifier allows illumination of the test object withlight of extremely low intensity. Moreover, the invention useswide-aperture aperture lens, with an f number as low as 1.2, or evenlower, further enabling the light from the source to be used mostefficiently. The use of a low-power laser is advantageous not onlybecause it is less expensive, but also because it avoids the safetyproblems associated with high-power lasers.

The present invention also enjoys significant advantages over thetechnique of electronic speckle pattern interferometry (ESPI). Thepresent invention requires only one beam, not two; no reference beam isneeded. There is thus no optical alignment problem as is present inESPI. It is also not necessary to adjust the ratio of intensities of theobject and reference beams. And because there is no reference beam, thepresent invention does not require special vibration isolationprecautions, thus allowing the technique to be employed in a productionor field environment. To the extent that the test object is a rigidbody, the interference pattern formed by the sheared images will begenerally insensitive to slight movements of the equipment.

With the present invention, the coherent length requirement of the beamis relatively low. In the case of holography or ESPI, the original beamis split into two beams before the object is illuminated, requiring thematching of the path lengths of the object beam and the reference beam.In the present invention, the path lengths are automatically matched;they originate from two nearby points on the object. Thus, it is notnecessary to use a relatively expensive, single-mode laser having a longcoherence length. Indeed, it is possible to practice the inventionwithout a laser at all, as long as the radiation used is reasonablycoherent. The degree of coherence required depends, in part, on theamount of ambient light. If the ambient light is very strong, therequirement of coherence is greater.

the present invention is particularly useful in nondestructive testingbecause it directly measures strains in the test object. Prematurefailures in defective components are usually due to stresses caused bythe defects. These stresses are directly related to strains, which areobserved directly.

While the invention has been described with respect to a specificembodiment, it is understood that the invention can be varied. Theinvention is not limited to particular type of birefringent material,nor is it limited to particular means of assembly of the opticalcomponents. The birefringent material may conveniently be mounted on thelens, but it may also be distinct from the lens. In certain cases, itmay even be possible to eliminate the lens entirely. Also, the conceptof the invention is not limited to the use of birefringent materials,but should be interpreted to include any other means, or material, fortransforming a pair of non-parallel beams, from distinct points on anobject, into a pair of nearly parallel, interfering beams. The inventionis also not limited by the type of computer employed. These and othersimilar modifications should be considered within the spirit and scopeof the following claims.

What is claimed is:
 1. A method of measuring displacement between twopoints on a test object, comprising the steps of:(a) generating a firstinterference pattern representing the superposition oflaterally-displaced images of the test object, while the object is in anundeformed state, (b) generating a sequence of second interferencepatterns representing the superposition of laterally-displaced images ofthe test object, while the object is in a deformed state, and repeatedlyproducing third interference patterns determined by comparing each ofsaid second interference patterns with the first interference pattern,the generating steps comprising the steps of storing the patterns in acomputer, the comparing step being performed by electronically comparingthe respective second patterns with the first pattern, (c) selecting apoint on one of the third interference patterns corresponding to thepoints on the test object, (d) adjusting an optical element so as toadjust the phase of the second interference patterns currently beingformed, by a measured amount, until the corresponding third interferencepattern comprises a fringe pattern having an extremum at the selectedpoint, and (e) converting the measured amount of phase adjustment into avalue of the displacement between the points on the object.
 2. Themethod of claim 1, wherein the optical element includes a polarizer, andwherein the first and second interference patterns are generated by thesteps of:(a) directing coherent radiation onto the test object, (b)passing radiation reflected from the object through a birefringentmaterial and then through the polarizer, and (c) directing radiationemerging from the polarizer onto a detector, the birefringent materialand the polarizer cooperating to form a random interference pattern onthe detector, and storing the random interference pattern thus formed.3. The method of claim 2, wherein the adjusting step comprises the stepof varying the orientation of the polarizer.
 4. The method of claim 2,wherein there is a quarter-wave plate disposed between the birefringentmaterial and the polarizer.
 5. A method of measuring displacementbetween two points on a test object, comprising the steps of:(a)generating a first interference pattern representing the superpositionof laterally-displaced images of the test object, while the object is inan undeformed state, the interference pattern being generating bydirecting radiation onto the test object, passing radiation reflectedfrom the object through a birefringent material and then through apolarizer, and directing radiation emerging from the polarizer onto adetector, the birefringent material and the polarizer cooperating toform a random interference pattern on the detector, and storing therandom interference pattern thus formed, (b) generating a sequence ofsecond interference patterns representing the superposition oflaterally-displaced images of the test object, while the object is in adeformed state, each second interference pattern being generated by thesame method used to generate the first interference pattern, (c)repeatedly producing third interference patterns determined by comparingeach of said second interference patterns with the first interferencepattern, the generating steps comprising the steps of storing thepatterns in a computer, the comparing step being performed byelectronically comparing the respective second patterns with the firstpattern. (d) selecting a point on one of the third interference patternscorresponding to the points on the test object, (e) adjusting theorientation of the polarizer so as to adjust the phase of the secondinterference patterns currently being formed, by a measured amount,until the corresponding third interference pattern comprises a fringepattern having an extremum at the selected point, and (f) converting themeasured amount of phase adjustment into a value of the displacementbetween the points on the object.
 6. The method of claim 5, whereinthere is a quarter-wave plate disposed between the birefringent materialand the polarizer.
 7. A method of measuring displacement between twopoints on a test object, comprising the steps of:(a) generating a firstinterference patter representing the superposition oflaterally-displaced images of the test object, while the object is in anundeformed state, the interference pattern being generated by directingradiation onto the test object, passing radiation reflected from theobject through a birefringent material, through a quarter-wave plate,and then through a polarizer, and directing radiation emerging from thepolarizer onto a detector, the birefringent material and the polarizercooperating to form a random interference pattern on the detector, andstoring the random interference pattern thus formed, (b) generating asequence of second interference patterns representing the superpositionof laterally-displaced images of the test object, while the object is ina deformed state, each second interference pattern being generating bythe same method used to generate the first interference pattern, (c)repeatedly producing third interference patterns determined by comparingeach of said second interference patterns with the first interferencepattern, the generating steps comprising the steps of storing thepatterns in a computer, the comparing step being performed byelectronically comparing the respective second patterns with the firstpattern, (d) selecting a point on one of the third interference patternscorresponding to the points on the test object, (e) adjusting theorientation of the polarizer so as to adjust the phase of the secondinterference patterns currently being formed, by a measured amount, byvarying the orientation of the polarizer, until the corresponding thirdinterference pattern comprises a fringe pattern having an extremum atthe selected point, and (f) converting the measured amount of phaseadjustment into a value of the displacement between the points on theobject.